A Comparative Statistical Study of the Methods of Weighting Observations

Abstract

The simple arithmetic mean is generally accepted as the most probable value. However, in a set of a small number of observations, a weighted mean is often regarded as being better than the simple arithmetic mean, even if the latter were obtained after rejecting the outlying observations. A number of methods of weighting have been put forward from time to time. This paper presents the result of a statistical study designed to discover whether any of the weighting methods produce values superior to the simple arithmetic mean. The study follows the same lines as a previous paper [Oswal and Tiwari 1965]. Of the six methods compared, only that of Jeffreys has been found to give values statistically superior to the simple arithmetic mean. The use of Jeffreys’ mean is suggested, therefore, for survey work, especially if these values are required for further rigorous adjustment purposes.